This was 1966, and they wrote SciFi just like they did westerns.
Roddenberry wrote it/had it written that way because he knew Westerns, but didn't know anything about Sci Fi; I think it's his wife who said this and said that the same script works if they have revolvers and horses rather than phasors and space ships.
@Northwest Actually, Roddenberry did write several, and he also came up with the idea; from the IMDB's info on TOS (https://m.imdb.com/title/tt0060028/fullcredits/?ref_=tt_cst_sm):
And since there had been a huge wave of Westerns on TV & in film, I'm guessing it was also a comfortable spot for others involved. He had experience noted in the Wikipedia article (https://en.m.wikipedia.org/wiki/Star_Trek:_The_Original_Series):
Roddenberry had extensive experience in writing for series about the Old West that had been popular television fare in the 1950s and 1960s. Armed with this background, he characterized the new show in his first draft as "Wagon Train to the stars".[8][12] Like the familiar Wagon Train, each episode was to be a self-contained adventure story, set within the structure of a continuing voyage through space.
(The IMDB bears out his writing background.)
And while he hadn't worked on a bunch of Sci-Fi, it seems it was an early passion of his. Theodore Sturgeon write two episodes (and Shari Lewis wrote one!).
Here's more of the wikipedia on the influences Roddenberry cited:
Roddenberry noted a number of influences on his idea, some of which includes A. E. van Vogt's tales of the spaceship Space Beagle, Eric Frank Russell's Marathon series of stories, and the film Forbidden Planet (1956). Some have also drawn parallels with the television series Rocky Jones, Space Ranger (1954), a space opera that included many of the elements integral to Star Trek—the organization, crew relationships, missions, part of the bridge layout, and some technology.[7]:24 Roddenberry also drew heavily from C. S. Forester's Horatio Hornblower novels that depict a daring sea captain who exercises broad discretionary authority on distant sea missions of noble purpose. He often humorously referred to Captain Kirk as "Horatio Hornblower in Space".[11]
